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This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, we can consider solutions such that the curvature of the initial free surface does not belong to The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. We first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then we use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.

Monitoring streamflow velocity is of paramount importance for water resources management and in engineering practice. To this aim, image-based approaches have proved to be reliable systems to non-intrusively monitor water bodies in remote places at variable flow regimes. Nonetheless, to tackle their computational and energy requirements, offload processing and high-speed internet connections in the monitored environments, which are often difficult to access, is mandatory hence limiting the effective deployment of such techniques in several relevant circumstances. In this paper, we advance and simplify streamflow velocity monitoring by directly processing the image stream in situ with a low-power embedded system. By leveraging its standard parallel processing capability and exploiting functional simplifications, we achieve an accuracy comparable to state-of-the-art algorithms that typically require expensive computing devices and infrastructures. The advantage of monitoring streamflow velocity in situ with a lightweight and cost-effective embedded processing device is threefold. First, it circumvents the need for wideband internet connections, which are expensive and impractical in remote environments. Second, it massively reduces the overall energy consumption, bandwidth and deployment cost. Third, when monitoring more than one river section, processing “at the very edge” of the system efficiency improves scalability by a large margin, compared to offload solutions based on remote or cloud processing. Therefore, enabling streamflow velocity monitoring in situ with low-cost embedded devices would foster the widespread diffusion of gauge cameras even in developing countries where appropriate infrastructure might be not available or too expensive.

In this paper, a new particle tracer for surface hydrology is proposed. The approach leverages the complementary advantages offered by particle‐tracking velocimetry and traditional tracing technologies, such as dyes and chemicals, toward a practically feasible and low‐cost measurement system. Specifically, the proposed methodology is based on the detection and tracking of buoyant fluorescent microspheres through an experimental system that incorporates ultraviolet lamps to elicit the fluorescence response and a digital camera to record the particle transit. This low‐cost measurement system can be used in a variety of natural settings ranging from small‐scale streams to rills with scales on the order of a few centimeters in hillslopes. The use of insoluble buoyant particles reduces the amount of tracing material for experimental measurements. Further, particles' enhanced fluorescence allows for noninvasive flow characterization, that is, for nonintrusively detecting the tracer without deploying probes and samplers in the water. A proof of concept experiment for the proposed methodology is conducted on the Rio Cordon, a natural mountainous stream in the Italian Alps. Flow measurements at selected stream cross sections and travel time experiments on varying stream reaches are performed to ascertain the feasibility of fluorescent particle tracers. Such experimental findings demonstrate that the particles are visible in complex natural streams and are effective in estimating flow velocities and travel times. Key Points Fluorescent microspheres can be used as particle tracers in natural streams Flow velocity and travel time can be estimated using fluorescent particles The proof of concept of a new low cost measurement system is presented

Addressing the critical need for precise streamflow measurements in hydro-environmental research, this study evaluates large-scale particle image velocimetry (LSPIV) using cost-effective closed-circuit television (CCTV) cameras, providing a detailed sensitivity analysis in both laboratory and real-world canal settings. In laboratory conditions, a 45° camera angle notably enhanced performance, exhibiting a 12% decrease in MAE and a remarkable 40% reduction in RMSE compared to the performance of orthographic form. Tracer particles further enhanced LSPIV accuracy, decreasing both mean absolute error (MAE) and root mean square error (RMSE) by around 0.05 m/s. Optimal velocity coefficients for the lab ranged between 0.85 and 0.90. Nighttime measurements, using projection-based illumination, showed a minor 3% MAE variation and 0.02 RMSE difference versus daytime. In field experiments, a 45° upstream CCTV camera configuration notably improved LSPIV accuracy, achieving a 3% MAE and 0.055 m/s RMSE. For best results across different turbidity levels, we recommend a velocity coefficient range of 0.84 to 0.88. This study highlights the robustness and cost-efficiency of LSPIV as a transformative method for streamflow gauging, demonstrating its wide applicability in diverse hydro-environmental scenarios.

Image velocimetry has become an effective method of mapping flow conditions in rivers, but this analysis is typically performed in a post-processing mode after data collection is complete. In this study, we evaluated the potential to infer flow velocities in approximately real time as thermal images are being acquired from an uncrewed aircraft system (UAS). The sensitivity of thermal image velocimetry to environmental conditions was quantified by conducting 20 flights over four days and assessing the accuracy of image-derived velocity estimates via comparison to direct field measurements made with an acoustic Doppler current profiler (ADCP). This analysis indicated that velocity mapping was most reliable when the air was cooler than the water. We also introduced a workflow for River Velocity Measurement in Approximately Real Time (RiVMART) that involved transferring brief image sequences from the UAS to a ground station as distinct data packets. The resulting velocity fields were as accurate as those generated via post-processing. A new particle image velocimetry (PIV) algorithm based on staggered image sequences increased the number of image pairs available for a given image sequence duration and slightly improved accuracy relative to a standard PIV implementation. Direct, automated geo-referencing of image-derived velocity vectors based on information on the position and orientation of the UAS acquired during flight led to poor alignment with vectors that were geo-referenced manually by selecting ground control points from an orthophoto. This initial proof-of-concept investigation suggests that our workflow could enable highly efficient characterization of flow fields in rivers and might help support applications that require rapid response to changing conditions.

The main objective of wastewater treatment plants (WWTPs) is to remove pathogens, nutrients, organics, and other pollutants from wastewater. After these contaminants are partially or fully removed through physical, biological, and/or chemical processes, the treated effluents are discharged into receiving waterbodies. However, since WWTPs cannot remove all contaminants, especially those of emerging concern, they inevitably represent concentrated point sources of residual contaminant loads into surface waters. To understand the severity and extent of the impact of treated-wastewater discharges from such facilities into rivers and lakes, as well as to identify opportunities of improved management, detailed information about WWTPs is required, including (1) their explicit geospatial locations to identify the waterbodies affected and (2) individual plant characteristics such as the population served, flow rate of effluents, and level of treatment of processed wastewater. These characteristics are especially important for contaminant fate models that are designed to assess the distribution of substances that are not typically included in environmental monitoring programs. Although there are several regional datasets that provide information on WWTP locations and characteristics, data are still lacking at a global scale, especially in developing countries. Here we introduce a spatially explicit global database, termed HydroWASTE, containing 58 502 WWTPs and their characteristics. This database was developed by combining national and regional datasets with auxiliary information to derive or complete missing WWTP characteristics, including the number of people served. A high-resolution river network with streamflow estimates was used to georeference WWTP outfall locations and calculate each plant's dilution factor (i.e., the ratio of the natural discharge of the receiving waterbody to the WWTP effluent discharge). The utility of this information was demonstrated in an assessment of the distribution of treated wastewater at a global scale. Results show that 1 200 000 km of the global river network receives wastewater input from upstream WWTPs, of which more than 90 000 km is downstream of WWTPs that offer only primary treatment. Wastewater ratios originating from WWTPs exceed 10 % in over 72 000 km of rivers, mostly in areas of high population densities in Europe, the USA, China, India, and South Africa. In addition, 2533 plants show a dilution factor of less than 10, which represents a common threshold for environmental concern. HydroWASTE can be accessed at https://doi.org/10.6084/m9.figshare.14847786.v1 (Ehalt Macedo et al., 2021).

The Iowa Flood Center (IFC), established following the 2008 record floods, has developed a real-time flood forecasting and information dissemination system for use by all Iowans. The system complements the operational forecasting issued by the National Weather Service, is based on sound scientific principles of flood genesis and spatial organization, and includes many technological advances. At its core is a continuous rainfall–runoff model based on landscape decomposition into hillslopes and channel links. Rainfall conversion to runoff is modeled through soil moisture accounting at hillslopes. Channel routing is based on a nonlinear representation of water velocity that considers the discharge amount as well as the upstream drainage area. Mathematically, the model represents a large system of ordinary differential equations organized to follow river network topology. The IFC also developed an efficient numerical solver suitable for high-performance computing architecture. The solver allows the IFC to update forecasts every 15 min for over 1,000 Iowa communities. The input to the system comes from a radar-rainfall algorithm, developed in-house, that maps rainfall every 5 min with high spatial resolution. The algorithm uses Level II radar reflectivity and other polarimetric data from the Weather Surveillance Radar-1988 Dual-Polarimetric (WSR-88DP) radar network. A large library of flood inundation maps and real-time river stage data from over 200 IFC “stream-stage sensors” complement the IFC information system. The system communicates all this information to the general public through a comprehensive browser-based and interactive platform. Streamflow forecasts and observations from Iowa can provide support for a similar system being developed at the National Water Center through model intercomparisons, diagnostic analyses, and product evaluations.

Water velocity and discharge are essential parameters for monitoring water resources sustainably. Datasets acquired from Unoccupied Aerial Systems (UAS) allow for river monitoring at high spatial and temporal resolution, and may be the only alternative in areas that are difficult to access. Image or video-based methods for river flow monitoring have become very popular since they are not time-consuming or expensive in contrast to traditional methods. This study presents a non-contact methodology to estimate streamflow based on data collected from UAS. Both surface velocity and river geometry are measured directly in field conditions via the UAS while streamflow is estimated with a new technique. Specifically, surface velocity is estimated by using image-based velocimetry software while river bathymetry is measured with a floating sonar, tethered like a pendulum to the UAV. Traditional field measurements were collected along the same cross-section of the Aggitis River in Greece in order to assess the accuracy of the remotely sensed velocities, depths, and discharges. Overall, the new technique is very promising for providing accurate UAV-based streamflow results compared to the field data.

Reducing uncertainty in streamflow simulation is vital for effective water resource management. The impact of uncertainty in model calibration data (discharge), commonly derived from the rating curve, is often overlooked. This study applies the Monte Carlo simulation technique (MCST) to assess uncertainty in the rating curve. Advanced machine learning (ML) models, bidirectional long short-term memory (BiLSTM), and bidirectional gated recurrent units (BiGRUs) were used comparatively to evaluate the propagation of this uncertainty onto streamflow simulation on both daily and monthly temporal scales. Different sets of streamflow data, derived from the fitted curve and its lower and upper uncertainty bands, were utilized to train ML models independently. The results show the substantial impact of rating curve uncertainty in streamflow simulations, with the BiGRU model surpassing the BiLSTM model on both scales. As a result, the uncertainty in the rating curve results in an uncertainty of the streamflow of up to 30 and 25% on daily and monthly simulations, respectively. These findings underscore the importance of considering rating curve uncertainty in streamflow simulation to ensure accurate and reliable results. Therefore, streamflow should be treated as an uncertain variable and managed by incorporating rating curve uncertainty in decision-making.

The hydrology and hydrography of the Canadian Prairies are complex and difficult to represent in hydrological models. Recent studies suggest that runoff velocities on the Canadian Prairies may be much smaller than generally assumed. Times to peak, basin-scale flow velocities and roughnesses were derived from hourly streamflow hydrographs from 23 basins in the central Alberta Prairies. The estimated velocities were much smaller than would be estimated from most commonly used empirical equations, suggesting that many existing methods are not suitable for estimating times to peak or lag times in these basins. Basin area was found to be a poor predictor of basin-scale rainfall-runoff flow velocity. Estimated velocities generally increased with basin scale, indicating that slow basin responses at small scales could be related to the predominance of overland and/or shallow sub-surface flow over the very level topography. Basin-scale values of Manning's roughness parameter were found to be orders of magnitude greater than values commonly used for streams in other parts of the world. The very large values of roughness call into question whether the Manning equation should be used to calculate runoff in the prairies. These results have important implications for calculating rainfall runoff in this region since using widely published values of roughness will result in poor model estimation of streamflow hydrographs. It is likely that the Darcy–Weisbach equation, which is applicable to all flow regimes, may perform better in high-resolution hydrological models of this region. Further modelling and field research will be required to determine the physical causes of these very small basin-scale velocities.